def recenter(rv_constructor, *rv_args, **rv_kwargs):
if (rv_constructor.__name__ == 'Normal'
and not rv_kwargs['name'].startswith('y')):
# NB: assume everything is kwargs for now.
x_loc = rv_kwargs['loc']
x_scale = rv_kwargs['scale']
name = rv_kwargs['name']
shape = rv_constructor(*rv_args, **rv_kwargs).shape
a, b = get_or_init(name, shape) # w
kwargs_std = {}
kwargs_std['loc'] = tf.multiply(x_loc, a)
kwargs_std['scale'] = tf.pow(x_scale, b)
kwargs_std['name'] = name + '_param'
scale = tf.pow(x_scale, 1. - b)
b = tfb.AffineScalar(scale=scale,
shift=x_loc +
tf.multiply(scale, -kwargs_std['loc']))
if 'value' in rv_kwargs:
kwargs_std['value'] = b.inverse(rv_kwargs['value'])
rv_std = interceptable(rv_constructor)(*rv_args, **kwargs_std)
bijectors[name] = b
return b.forward(rv_std)
else:
return interceptable(rv_constructor)(*rv_args, **rv_kwargs)
def set_values(f, *args, **kwargs):
"""Sets random variable values to its aligned value."""
name = kwargs.get('name')
if name in model_kwargs:
kwargs['value'] = model_kwargs[name]
elif consumable_args:
kwargs['value'] = consumable_args.pop(0)
return interceptable(f)(*args, **kwargs)
def ncp(rv_constructor, *rv_args, **rv_kwargs):
if (rv_constructor.__name__ == 'Normal'
and not rv_kwargs['name'].startswith('y')):
loc = rv_kwargs['loc']
scale = rv_kwargs['scale']
name = rv_kwargs['name']
shape = rv_constructor(*rv_args, **rv_kwargs).shape
kwargs_std = {}
kwargs_std['loc'] = tf.zeros(shape)
kwargs_std['scale'] = tf.ones(shape)
kwargs_std['name'] = name + '_std'
b = tfb.AffineScalar(scale=scale, shift=loc)
if 'value' in rv_kwargs:
kwargs_std['value'] = b.inverse(rv_kwargs['value'])
rv_std = interceptable(rv_constructor)(*rv_args, **kwargs_std)
return b.forward(rv_std)
else:
return interceptable(rv_constructor)(*rv_args, **rv_kwargs)
def set_values(f, *args, **kwargs):
"""Sets random variable values to its aligned value."""
name = kwargs.get("name")
if name in model_kwargs:
kwargs["value"] = model_kwargs[name]
return interceptable(f)(*args, **kwargs)
def recenter(rv_constructor, *rv_args, **rv_kwargs):
rv_name = rv_kwargs.get('name')
rv_value = rv_kwargs.pop('value', None)
base_bijector = None
if rv_constructor.__name__ == 'TransformedDistribution':
if (rv_args[1].__class__.__name__ == 'Invert'
and rv_args[1].bijector.__class__.__name__ == 'SoftClip'):
distribution = rv_args[0]
base_bijector = rv_args[1].bijector
rv_constructor = distribution.__class__
rv_kwargs = distribution.parameters
rv_args = rv_args[2:]
# We were given a value for the transformed RV. Let's pretend it was
# for the original.
if rv_value is not None:
rv_value = base_bijector.forward(rv_value)
if (rv_constructor.__name__ == 'Normal'
and not rv_name.startswith('y')):
# NB: assume everything is kwargs for now.
x_loc = rv_kwargs['loc']
x_scale = rv_kwargs['scale']
name = rv_kwargs['name']
a, b, _ = get_or_init(name,
loc_shape=tf.shape(x_loc),
scale_shape=tf.shape(x_scale),
parameterisation_type='scalar')
kwargs_std = {}
kwargs_std['loc'] = tf.multiply(x_loc, a)
kwargs_std['scale'] = tf.pow(
x_scale, b) # tf.multiply(x_scale - 1., b) + 1.
kwargs_std['name'] = name
scale = x_scale / kwargs_std['scale'] # tf.pow(x_scale, 1. - b)
shift = x_loc - tf.multiply(scale, kwargs_std['loc'])
b = tfb.AffineScalar(scale=scale, shift=shift)
if rv_value is not None:
rv_value = b.inverse(rv_value)
learnable_parameters[name +
'_prior_mean'] = tf.convert_to_tensor(x_loc)
learnable_parameters[name + '_prior_scale'] = tf.convert_to_tensor(
x_scale)
# If original RV was constrained, transform the constraint to the new
# standardized RV. For now we assume a double-sided constraint.
if base_bijector is not None:
constraint_std = tfb.SoftClip(
low=b.inverse(base_bijector.low),
high=b.inverse(base_bijector.high),
hinge_softness=base_bijector.hinge_softness / scale
if base_bijector.hinge_softness is not None else None)
rv_std = edward2.TransformedDistribution(
rv_constructor(**kwargs_std),
tfb.Invert(constraint_std),
value=constraint_std.inverse(rv_value)
if rv_value is not None else None)
b = b(constraint_std)
else:
kwargs_std['value'] = rv_value
rv_std = interceptable(rv_constructor)(*rv_args, **kwargs_std)
bijectors[name] = b
return b.forward(rv_std)
elif ((rv_constructor.__name__.startswith('MultivariateNormal')
or rv_constructor.__name__.startswith('GaussianProcess'))
and not rv_kwargs['name'].startswith('y')):
name = rv_kwargs['name']
if rv_constructor.__name__.startswith('GaussianProcess'):
gp_dist = rv_constructor(*rv_args, **rv_kwargs).distribution
X = gp_dist._get_index_points()
x_loc = gp_dist.mean_fn(X)
x_cov = gp_dist._compute_covariance(index_points=X)
else:
x_loc = rv_kwargs['loc']
x_cov = rv_kwargs['covariance_matrix']
a, b, c = get_or_init(name,
loc_shape=tf.shape(x_loc),
scale_shape=tf.shape(x_cov)[:-1],
parameterisation_type=parameterisation_type)
ndims = tf.shape(x_cov)[-1]
x_loc = tf.broadcast_to(x_loc, tf.shape(x_cov)[:-1])
cov_dtype = tf.float64 if FLAGS.float64 else x_cov.dtype
x_cov = tf.cast(x_cov, cov_dtype)
if parameterisation_type == 'eig':
"""Extra cost of the eigendecomposition?
we do the eig to get Lambda, Q.
We rescale Lambda and create the prior dist linop
- point one: the prior is an MVN (albeit an efficient one), where
in NCP it's just Normal
Then we construct the remaining scale matrix. (an n**3 matmul)
And unlike a cholesky factor these matrices aren't triangular, so
multiplication or division
- can we
"""
Lambda, Q = eigh_with_safe_gradient(x_cov)
Lambda = tf.abs(Lambda)
Lambda = tf.cast(Lambda, tf.float32)
Q = tf.cast(Q, tf.float32)
Lambda_hat_b = tf.pow(Lambda, b)
if tied_pparams:
# If the scale parameterization is in the eigenbasis,
# apply it to the mean in the same basis.
loc_in_eigenbasis = tf.linalg.matvec(Q,
x_loc,
adjoint_a=True)
reparam_loc = tf.linalg.matvec(
Q, tf.multiply(loc_in_eigenbasis, a))
else:
reparam_loc = tf.multiply(x_loc, a)
kwargs_std = {}
kwargs_std['loc'] = reparam_loc
kwargs_std['scale'] = LinearOperatorEigenScale(
Q, d=tf.sqrt(Lambda_hat_b))
kwargs_std['name'] = name
Q_linop = LinearOperatorOrthogonal(Q, det_is_positive=True)
scale = tf.linalg.LinearOperatorComposition([
Q_linop,
tf.linalg.LinearOperatorDiag(tf.sqrt(Lambda + 1e-10)),
tf.linalg.LinearOperatorDiag(
1. / tf.sqrt(Lambda_hat_b + 1e-10)),
Q_linop.adjoint(),
])
shift = x_loc - scale.matvec(reparam_loc)
b = tfb.AffineLinearOperator(scale=scale, shift=shift)
if 'value' in rv_kwargs:
kwargs_std['value'] = b.inverse(rv_kwargs['value'])
elif parameterisation_type == 'chol':
L = tf.linalg.cholesky(x_cov +
1e-6 * tf.eye(ndims, dtype=x_cov.dtype))
L = tf.cast(L, tf.float32)
reparam_loc = x_loc * a
reparam_scale = tf.linalg.LinearOperatorLowerTriangular(
tf.linalg.diag(1 - b) + b[..., tf.newaxis] * L)
kwargs_std = {}
kwargs_std['loc'] = reparam_loc
kwargs_std['scale'] = reparam_scale
kwargs_std['name'] = name
Dinv = tf.linalg.triangular_solve(
tf.cast(reparam_scale.to_dense(), cov_dtype),
tf.eye(ndims, dtype=cov_dtype))
Dinv = tf.cast(Dinv, tf.float32)
scale = tf.matmul(L, Dinv)
shift = x_loc - tf.linalg.matvec(scale, reparam_loc)
b = tfb.AffineLinearOperator(
scale=tf.linalg.LinearOperatorFullMatrix(scale),
shift=shift)
if 'value' in rv_kwargs:
kwargs_std['value'] = b.inverse(rv_kwargs['value'])
elif parameterisation_type == 'indep':
# Assumes `C^-1 = diag(c)` is a learned diagonal matrix of 'evidence
# precisions'. This approximates the true posterior under an iid
# Gaussian observation model:
prior_chol = tf.linalg.cholesky(x_cov)
prior_inv = tf.linalg.cholesky_solve(
prior_chol, tf.eye(ndims, dtype=prior_chol.dtype))
approx_posterior_prec = prior_inv + tf.cast(
tf.linalg.diag(c), prior_inv.dtype)
approx_posterior_prec_chol = tf.linalg.cholesky(
approx_posterior_prec)
approx_posterior_cov = tf.linalg.cholesky_solve(
approx_posterior_prec_chol,
tf.eye(ndims, dtype=approx_posterior_prec_chol.dtype))
cov_chol = tf.linalg.cholesky(approx_posterior_cov)
cov_chol = tf.cast(cov_chol, tf.float32)
prior_chol = tf.cast(prior_chol, tf.float32)
scale_linop = tf.linalg.LinearOperatorLowerTriangular(cov_chol)
reparam_loc = x_loc * a
reparam_scale = tf.linalg.LinearOperatorComposition([
tf.linalg.LinearOperatorInversion(scale_linop),
tf.linalg.LinearOperatorLowerTriangular(prior_chol)
])
kwargs_std = {}
kwargs_std['loc'] = reparam_loc
kwargs_std['scale'] = reparam_scale
kwargs_std['name'] = name
shift = x_loc - scale_linop.matvec(reparam_loc)
b = tfb.AffineLinearOperator(scale=scale_linop, shift=shift)
if 'value' in rv_kwargs:
kwargs_std['value'] = b.inverse(rv_kwargs['value'])
elif parameterisation_type == 'eigindep':
# Combines 'eig' and 'indep' parameterizations, modeling the posterior
# as
# (V D**(-b) V' + diag(c))^-1
# where VDV' is the eigendecomposition of the prior cov, and b and c
# are learned vectors.
b, c = [tf.cast(x, cov_dtype) for x in (b, c)]
Lambda, Q = eigh_with_safe_gradient(x_cov)
Lambda = tf.abs(Lambda)
Lambda_hat_b = 1e-6 + tf.pow(Lambda, b)
prior = tf.matmul(
Q,
tf.matmul(tf.linalg.diag(Lambda_hat_b), Q, adjoint_b=True))
prior_chol = tf.linalg.cholesky(
prior + 1e-6 * tf.eye(ndims, dtype=prior.dtype))
prior_prec = tf.linalg.cholesky_solve(
prior_chol + 1e-6 * tf.eye(ndims, dtype=prior_chol.dtype),
tf.eye(ndims, dtype=prior_chol.dtype))
approx_posterior_prec = prior_prec + tf.linalg.diag(c)
approx_posterior_prec_chol = tf.linalg.cholesky(
approx_posterior_prec)
approx_posterior_cov = tf.linalg.cholesky_solve(
approx_posterior_prec_chol + 1e-6 *
tf.eye(ndims, dtype=approx_posterior_prec_chol.dtype),
tf.eye(ndims, dtype=approx_posterior_prec_chol.dtype))
cov_chol = tf.linalg.cholesky(
approx_posterior_cov +
1e-6 * tf.eye(ndims, dtype=approx_posterior_cov.dtype))
cov_chol = tf.cast(cov_chol, tf.float32)
prior_chol = tf.cast(prior_chol, tf.float32)
scale_linop = tf.linalg.LinearOperatorLowerTriangular(cov_chol)
reparam_loc = tf.multiply(x_loc, a)
reparam_scale = tf.linalg.LinearOperatorComposition([
tf.linalg.LinearOperatorInversion(scale_linop),
tf.linalg.LinearOperatorLowerTriangular(prior_chol)
])
kwargs_std = {}
kwargs_std['loc'] = reparam_loc
kwargs_std['scale'] = reparam_scale
kwargs_std['name'] = name
shift = x_loc - scale_linop.matvec(reparam_loc)
b = tfb.AffineLinearOperator(scale=scale_linop, shift=shift)
if 'value' in rv_kwargs:
kwargs_std['value'] = b.inverse(rv_kwargs['value'])
else:
raise Exception('unrecognized reparameterization strategy!')
if rv_constructor.__name__.startswith('GaussianProcess'):
rv_std = edward2.MultivariateNormalLinearOperator(
*rv_args, **kwargs_std)
else:
rv_std = interceptable(rv_constructor)(*rv_args, **kwargs_std)
bijectors[name] = b
return b.forward(rv_std)
else:
return interceptable(rv_constructor)(*rv_args, **rv_kwargs)
def ncp(rv_constructor, *rv_args, **rv_kwargs):
base_bijector = None
rv_value = rv_kwargs.pop('value', None)
if rv_constructor.__name__ == 'TransformedDistribution':
if (rv_args[1].__class__.__name__ == 'Invert'
and rv_args[1].bijector.__class__.__name__ == 'SoftClip'):
distribution = rv_args[0]
base_bijector = rv_args[1].bijector
rv_constructor = distribution.__class__
rv_kwargs = distribution.parameters
rv_args = rv_args[2:]
# We were given a value for the transformed RV. Let's pretend it was
# for the original.
if rv_value is not None:
rv_value = base_bijector.forward(rv_value)
if (rv_constructor.__name__ == 'Normal'
and not rv_kwargs['name'].startswith('y')):
loc = rv_kwargs['loc']
scale = rv_kwargs['scale']
name = rv_kwargs['name']
kwargs_std = {}
kwargs_std['loc'] = tf.zeros_like(loc)
kwargs_std['scale'] = tf.ones_like(scale)
kwargs_std['name'] = name + '_std'
b = tfb.AffineScalar(scale=scale, shift=loc)
if rv_value is not None:
rv_value = b.inverse(rv_value)
kwargs_std['value'] = rv_value
rv_std = interceptable(rv_constructor)(*rv_args, **kwargs_std)
return b.forward(rv_std)
elif ((rv_constructor.__name__.startswith('MultivariateNormal')
or rv_constructor.__name__.startswith('GaussianProcess'))
and not rv_kwargs['name'].startswith('y')):
name = rv_kwargs['name']
if rv_constructor.__name__.startswith('GaussianProcess'):
gp_dist = rv_constructor(*rv_args, **rv_kwargs).distribution
X = gp_dist._get_index_points()
x_loc = gp_dist.mean_fn(X)
x_cov = gp_dist._compute_covariance(index_points=X)
shape = tfd.MultivariateNormalFullCovariance(x_loc,
x_cov).event_shape
else:
x_loc = rv_kwargs['loc']
x_cov = rv_kwargs['covariance_matrix']
shape = rv_constructor(*rv_args, **rv_kwargs).shape
kwargs_std = {}
kwargs_std['loc'] = tf.zeros(shape)
kwargs_std['scale_diag'] = tf.ones(shape[0])
kwargs_std['name'] = name + '_std'
scale = tf.linalg.cholesky(x_cov + 1e-6 * tf.eye(tf.shape(x_cov)[-1]))
b = tfb.AffineLinearOperator(
scale=tf.linalg.LinearOperatorLowerTriangular(scale), shift=x_loc)
if 'value' in rv_kwargs:
kwargs_std['value'] = b.inverse(rv_kwargs['value'])
rv_std = edward2.MultivariateNormalDiag(*rv_args, **kwargs_std)
return b.forward(rv_std)
else:
return interceptable(rv_constructor)(*rv_args, **rv_kwargs)
def trace(rv_constructor, *rv_args, **rv_kwargs):
rv = interceptable(rv_constructor)(*rv_args, **rv_kwargs)
name = rv_kwargs['name']
trace_result[name] = rv.value
return rv
